Aunt Martha is Kapugen's aunt, which makes her Miyax's great aunt. Although she's mentioned beforehand, she first turns up at the seal camp, where she insists that Miyax come with her back to Mekoryuk, so that the young girl can go to school.
Martha is just plain awful. There's no getting around it. She doesn't show Julie any affection whatsoever. Even when she tells Julie that her father has died, she does so bluntly, with her back toward Julie (2.40). Plus, she's super strict. Our narrator tells us, "Martha gave [Julie] chores to do on weekends and refused to let her attend the movies with her friends. The winter nights in the dark little house became nightmares" (2.60).
Additionally, she's a bit of a hypocrite. Although she previously insisted that Julie leave the seal camp and go to school, she still believes strongly in Eskimo traditions. So she scolds Julie for cutting her hair short and having friends like Judith. But then she tells Julie that she doesn't have to follow the Eskimo tradition of marrying Daniel if she doesn't want to. What gives? Is this just showing us how difficult it is to reconcile the two cultures (i.e., make them work together)?
All in all, she sounds like your basic horror, and we don't blame Miyax for leaving her and never looking back.